What is the Greatest Common Factor of 3105 and 3114?

Greatest common factor (GCF) of 3105 and 3114 is 9.

GCF(3105,3114) = 9

We will now calculate the prime factors of 3105 and 3114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3105 and 3114.

How to find the GCF of 3105 and 3114?

We will first find the prime factorization of 3105 and 3114. After we will calculate the factors of 3105 and 3114 and find the biggest common factor number .

Step-1: Prime Factorization of 3105

Prime factors of 3105 are 3, 5, 23. Prime factorization of 3105 in exponential form is:

3105 = 3³ × 5¹ × 23¹

Step-2: Prime Factorization of 3114

Prime factors of 3114 are 2, 3, 173. Prime factorization of 3114 in exponential form is:

3114 = 2¹ × 3² × 173¹

Step-3: Factors of 3105

List of positive integer factors of 3105 that divides 3105 without a remainder.

1, 3, 5, 9, 15, 23, 27, 45, 69, 115, 135, 207, 345, 621, 1035

Step-4: Factors of 3114

List of positive integer factors of 3114 that divides 3105 without a remainder.

1, 2, 3, 6, 9, 18, 173, 346, 519, 1038, 1557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3105 and 3114. The biggest common factor number is the GCF number.
So the greatest common factor 3105 and 3114 is 9.

Also check out the Least Common Multiple of 3105 and 3114